Abadi, Dian Savitri, Fajar Adi-Kusumo
In prey-predator models, nonlinear interaction between prey and predator populations results in oscillatory behavior that shows the dynamic growth of the populations. In the growth process, very often both prey and predator share the same resource in their habitat. This is an intraguild predation model. This study focuses on an intraguild prey-predator model generalized by introducing Holling type III functional response. The existence of biologically meaningful equilibria has been investigated. The stability analysis of the equilibria has been determined. Finally, bifurcation and numerical analyses have been presented to illustrate the dynamic behavior of the system. Taking the biotic resource enrichment as the bifurcation parameter, a Hopf bifurcation takes place, where solutions with limit cycle behavior appear. Varying further the parameter, a fold bifurcation of the limit cycle takes place, where the unstable limit appeared due to Hopf bifurcation reverses its growing direction and changes its stability. Taking the predation rate as the bifurcation parameter, saddle-node bifurcations take place. The existence of stable interior equilibria and stable periodic solutions, of which all prey and predator populations and the resource co-exist, guarantee the boundedness of the size of the populations and the resource. This is good from the conservation of an ecosystem point of view. © 2024 All rights reserved.
Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Negeri Surabaya, Surabaya, Indonesia; Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia
